Journal ArticleDOI
Perspectives and results on the stability and stabilizability of hybrid systems
R.A. Decarlo,Michael S. Branicky,Stefan Pettersson,Bengt Lennartson +3 more
- Vol. 88, Iss: 7, pp 1069-1082
TLDR
In this paper, the authors introduce the concept of hybrid systems and some of the challenges associated with the stability of such systems, including the issues of guaranteeing stability of switched stable systems and finding conditions for the existence of switched controllers for stabilizing switched unstable systems.Abstract:
This paper introduces the concept of a hybrid system and some of the challenges associated with the stability of such systems, including the issues of guaranteeing stability of switched stable systems and finding conditions for the existence of switched controllers for stabilizing switched unstable systems. In this endeavour, this paper surveys the major results in the (Lyapunov) stability of finite-dimensional hybrid systems and then discusses the stronger, more specialized results of switched linear (stable and unstable) systems. A section detailing how some of the results can be formulated as linear matrix inequalities is given. Stability analyses on the regulation of the angle of attack of an aircraft and on the PI control of a vehicle with an automatic transmission are given. Other examples are included to illustrate various results in this paper.read more
Citations
More filters
Journal ArticleDOI
Reachability and Controllability Analysis of Periodic Switched Boolean Control Networks
Journal ArticleDOI
Control of spatially distributed processes with unknown transport-reaction parameters via two layer system adaptations
TL;DR: In this article, a combination of a model order reduction approach and a Lyapunov-based adaptive control technique is used to address the control issues in the presence of unknown parameters of the system.
Controller synthesis for switched systems using approximate dynamic programming
TL;DR: Hu et al. as discussed by the authors developed an approximate dynamic programming (ADP) framework for solving optimal control and stabilization problems for a general discrete-time switched nonlinear system and showed that the solution generated by the ADP algorithm is exponentially stabilizing and sub-optimal.
Proceedings ArticleDOI
Stability analysis and design of uniform ultimate boundedness control for a class of nonlinear switched systems
TL;DR: A uniform ultimate boundedness controller is developed to guarantee the practical stability of the switched systems with the nonlinear and time-varying uncertain disturbance.
Proceedings ArticleDOI
On convergence rates of switched linear systems
Zhendong Sun,Robert Shorten +1 more
TL;DR: In this article, the authors introduce the concepts of best case and worst case convergence rates for switched linear systems, and their connections to the problems of stability and stabilization are briefly discussed.
References
More filters
Book
Applied Nonlinear Control
TL;DR: Covers in a progressive fashion a number of analysis tools and design techniques directly applicable to nonlinear control problems in high performance systems (in aerospace, robotics and automotive areas).
Book
Linear Matrix Inequalities in System and Control Theory
TL;DR: In this paper, the authors present a brief history of LMIs in control theory and discuss some of the standard problems involved in LMIs, such as linear matrix inequalities, linear differential inequalities, and matrix problems with analytic solutions.
Book
Differential Equations with Discontinuous Righthand Sides
TL;DR: The kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics, algebraic geometry interacts with physics, and such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes.